Ethnomathematics and the Diversification of Mathematics Teaching
Dr. Karen François, Director of the Centre for Logic and Philosophy of Science and the Doctoral School of Human Sciences, Vrije Universiteit Brussel, Belgium
As a field of enquiry, ethnomathematics started in the 1960s, its subject being the mathematical practices of so-called illiterate or, more politically correctly, non-literate peoples, holding that mathematical ideas are pan-human and are primarily developed within cultures. Based on their empirical investigations, mathematician Marcia Ascher and anthropologist Robert Ascher1 demonstrated that the local mathematical practices in question and ‘our’ Western ones are equally complex. Brazilian mathematician and educationalist Ubiratàn D’Ambrosio was the first to propose a research program for ethnomathematics. As the intellectual father of the research field of ethnomathematics, D’Ambrosio provided in the late 1990s a more extended version of the concept of ethnomathematics, with his aim being the encompassing of a range of cultures. He presupposed “a broader concept of ethno to include all culturally identifiable groups with their jargons, codes, symbols, myths, and even specific ways of reasoning and inferring”.2 Following this, the research interests of the newly founded discipline pertain to the development, transmission, and distribution of mathematical knowledge as dynamic processes embedded in socio-cultural contexts. An important implication is that Western mathematics is also considered as having developed, and as continuing to develop, within a particular, contextual reality — not detached from it.
The Impact of Cultural Differences on Mathematics Education Globally
International comparative research on mathematical literacy reveals cultural and language background biases. François and Pinxten3 started to discuss cultural biases in mathematics curriculum and international comparative research, questioning whether dropout rates could be understood and hence mended against the intuitive and otherwise culturally framed background knowledge of the pupils who ‘fail’. The answer is clearly to reset the curriculum to meet the diversification of intuitions and (slightly) other reasoning styles and practices of peoples. Small differences allow people to cope with reality and survive, notwithstanding the manifest differences in perspective on reality. An interesting example, as studied with Navaho Native Americans by the anthropologist Pinxten, is language differences and their implications for mathematical reasoning. In the verb-languages of this world (those languages that are without a genuine noun category, that is) the intuition is that of a world of events or processes, rather than things or static phenomena. Now try to imagine set theory without ‘objects’ like sets and elements but rather built up on changes and events.
Ethnomathematics and Mathematics Education
Ethnomathematics or the implementation of local mathematical practices in the formal mathematics curriculum is in line with the social turn within learning theory and the emphasis on the fusion of the learning process into a sociocultural environment. Social sciences have developed, during the last decades, three main learning theories, each of them with a specific focus on the learning process. Whereas behaviorism focuses on the input-output mechanisms, ignoring the black box in between, genetic psychology mainly focuses on the black box and what is going on in the student’s mind. The socio-cultural theory considers the environment in which the learning process is taking place. The social turn within the learning theory became of interest in the field of mathematics education mostly as a reaction to the huge dropping out of pupils with a specific socio-cultural background. Sociocultural theory elaborates on the learning theory of the Russian Lev Vygotsky and his concept of a zone of proximal learning as developed in the 1970s. The concept can be understood as the cognitive field of the pupil, which can be spotted at the fringe of the background knowledge and the out-of-school worldview. It is the zone of learning where the pupil will be able to connect insightfully to new knowledge because of the intrinsic relation between background knowledge and new inputs. Background and out-of-school knowledge are integrated in formal learning as a stepping-stone for acquiring new knowledge, new meanings, and new mental frames.4
Mindful Education beyond the Classroom
Ethnomathematics is a practice that goes beyond the classroom — it is the practice and the knowledge that pupils learn out of school. Social learning theory emphasizes that pupils do not come to school as empty barrels. They do bring their background and out-of-school knowledge into the classroom. Teachers, at all levels, have to invest igate the background knowledge that children actually bring to school and they have to investigate how to introduce pupils’ learning context in the teaching of mathematics at school. Ignorance concerning the local culture, local practices, and knowledge may well explain the gap between success and failure in a formal mathematics classroom.
Indeed, when we agree that children are raised throughout the world in the particular meaning production processes and mental frames of their particular environment, it is important and sensible (that is, possibly beneficial) to take into account — and even actively study — the contents and the learning strategies of the out-ofschool knowledge and skills the child possesses and uses when first coming into contact with what Western educators call mathematics education.5
Endnotes
1 Marcia Ascher and Robert Ascher, “Ethnomathematics,” in
Ethnomathematics: Challenging Eurocentrism in Mathematics Education,
ed. Arthur B. Powell and Marilyn Frankenstein (Albany: State University of
New York Press — SUNY, [1986] 1997), 25–50.
2 Ubiratàn D’Ambrosio, “Ethnomathematics and its Place in the
History and Pedagogy of Mathematics,” in Ethnomathematics: Challenging
Eurocentrism in Mathematics Education, ed. Arthur B. Powell and Marilyn
Frankenstein (Albany: State University of New York Press — SUNY, [1986] 1997), 13–24.
3 Karen François and Rik Pinxten, “Multimathemacy: Time to Reset?”
(Mathematics Education and Life at Times of Crisis. Proceedings of the Ninth
International Mathematics Education and Society Conference — MES — Vol. 2,
480–490), ed. Anna Chronaki. Book Series: Mathematics Education and
Society. Volos, Greece, 7–12 April 2017.
4 Ibid.
5 Ibid.
